Autocorrelate Your Assets or, It's Not All White Noise: A Practical Means for Generating Autocorrelated Time Series Data in Monte Carlo Simulations

Abstract

The inherent assumption with most Monte Carlo techniques is that one may ignore autocorrelations, but doing so compromises the quality of the prediction from the data. Simulations that do not take account of autocorrelation will not properly model reality, as there is significant autocorrelation in many asset returns, for example in T-Bills and hedge fund strategies that involve illiquid, long-term holdings, which do not satisfy the “random walk” assumption with a “white noise” spectrum. A detailed mathematical method is proposed for simulating market returns by generating random time series that satisfy the statistics of any serial autocorrelation, as well as the actual (possibly non-Gaussian) joint probability distributions.